Local Discontinuous Galerkin Methods to a Dispersive System of KdV-Type Equations

Chao Zhang; Yan Xu; Yinhua Xia

doi:10.1007/s10915-020-01370-2

Local Discontinuous Galerkin Methods to a Dispersive System of KdV-Type Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01370-2 ◽

2021 ◽

Vol 86 (1) ◽

Author(s):

Chao Zhang ◽

Yan Xu ◽

Yinhua Xia

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Dispersive System ◽

Kdv Type Equations

Download Full-text

Local discontinuous Galerkin methods for the Kuramoto–Sivashinsky equations and the Ito-type coupled KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2005.06.021 ◽

2006 ◽

Vol 195 (25-28) ◽

pp. 3430-3447 ◽

Cited By ~ 66

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Kdv Equations ◽

Local Discontinuous Galerkin Methods ◽

Coupled Kdv Equations

Download Full-text

Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2015068 ◽

2016 ◽

Vol 50 (4) ◽

pp. 1083-1105 ◽

Cited By ~ 21

Author(s):

Haijin Wang ◽

Shiping Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

Download Full-text

Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Cited By ~ 7

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

High Order ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

Download Full-text

Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-019-01072-4 ◽

2019 ◽

Vol 81 (3) ◽

pp. 2080-2114 ◽

Cited By ~ 4

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes ◽

Diffusion Problems

Download Full-text

Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation

Journal of Computational Physics ◽

10.1016/j.jcp.2019.109002 ◽

2020 ◽

Vol 401 ◽

pp. 109002 ◽

Cited By ~ 4

Author(s):

Xiaole Li ◽

Weizhou Sun ◽

Yulong Xing ◽

Ching-Shan Chou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Boussinesq Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

Download Full-text

Local discontinuous Galerkin methods for the generalized Zakharov system

Journal of Computational Physics ◽

10.1016/j.jcp.2009.10.029 ◽

2010 ◽

Vol 229 (4) ◽

pp. 1238-1259 ◽

Cited By ~ 23

Author(s):

Yinhua Xia ◽

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Zakharov System ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

Download Full-text

Efficient multigrid solution of elliptic interface problems using viscosity-upwinded local discontinuous Galerkin methods

Communications in Applied Mathematics and Computational Science ◽

10.2140/camcos.2019.14.247 ◽

2019 ◽

Vol 14 (2) ◽

pp. 247-283

Author(s):

Robert I. Saye

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Interface Problems ◽

Galerkin Methods ◽

Elliptic Interface Problems ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

Download Full-text

Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes

BIT Numerical Mathematics ◽

10.1007/s10543-019-00757-4 ◽

2019 ◽

Vol 59 (4) ◽

pp. 853-876 ◽

Cited By ~ 1

Author(s):

Jie Du ◽

Yang Yang ◽

Eric Chung

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

Download Full-text

Local Discontinuous Galerkin Methods for the $$\mu $$ μ -Camassa–Holm and $$\mu $$ μ -Degasperis–Procesi Equations

Journal of Scientific Computing ◽

10.1007/s10915-018-0891-7 ◽

2018 ◽

Vol 79 (2) ◽

pp. 1294-1334 ◽

Cited By ~ 2

Author(s):

Chao Zhang ◽

Yan Xu ◽

Yinhua Xia

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

Download Full-text

Local Discontinuous Galerkin Methods for the Functionalized Cahn–Hilliard Equation

Journal of Scientific Computing ◽

10.1007/s10915-014-9920-3 ◽

2014 ◽

Vol 63 (3) ◽

pp. 913-937 ◽

Cited By ~ 10

Author(s):

Ruihan Guo ◽

Yan Xu ◽

Zhengfu Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Hilliard Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Cahn Hilliard Equation

Download Full-text